Step 1: Coordination number is defined as the number of ligand donor atoms directly bonded to the central metal atom.
Step 2: In the complex \([\text{PtCl}(\text{C}_5\text{H}_5\text{N})(\text{NH}_3)]\), the ligands present are:
\begin{itemize}
\item \(\text{Cl}^-\) : monodentate ligand (1 donor atom)
\item \(\text{C}_5\text{H}_5\text{N}\) (pyridine): monodentate ligand (1 donor atom)
\item \(\text{NH}_3\): monodentate ligand (1 donor atom)
\end{itemize}
Step 3: Total number of donor atoms attached to platinum:
\[
1 + 1 + 1 = 3
\]
Step 4: Hence, the coordination number of platinum is 3.